Bayesianism
http://slatestarcodex.com/2016/09/12/its-bayes-all-the-way-up/ Bayes Theorem Bayes' theorem is a law relating conditional probabilities of two events using their unconditioned (prior) probabilities. (coming soon) In Science Bayesian inference is becoming more accepted in science, but the dominant trends still do not employ Bayesian logic implicitly. Why most of psychology is statistically unfalsifiable - Richard D Morey, Medium Criticism |NewYoker://What Nate Silver Gets Wrong> By Gary Marcus and Ernest Davis, January 25, 2013 "A Bayesian approach is particularly useful when predicting outcome probabilities in cases where one has strong prior knowledge of a situation. Suppose, for instance (borrowing an old example that Silver revives), that a woman in her forties goes for a mammogram and receives bad news: a “positive” mammogram. However, since not every positive result is real, what is the probability that she actually has breast cancer? To calculate this, we need to know four numbers. The fraction of women in their forties who have breast cancer is 0.014, which is about one in seventy. The fraction who do not have breast cancer is therefore 1 - 0.014 = 0.986. These fractions are known as the prior probabilities. The probability that a {person} who has breast cancer will get a positive result on a mammogram is 0.75. The probability that a {person} who does not have breast cancer will get a false positive on a mammogram is 0.1. These are known as the conditional probabilities. Applying Bayes’s theorem, we can conclude that, among {people} who get a positive result, the fraction who actually have breast cancer is (0.014 x 0.75) / ((0.014 x 0.75) + (0.986 x 0.1)) = 0.1, approximately. That is, once we have seen the test result, the chance is about ninety per cent that it is a false positive. In this instance, Bayes’s theorem is the perfect tool for the job." "But the Bayesian approach is much less helpful when there is no consensus about what the prior probabilities should be. For example, in a notorious series of experiments, Stanley Milgram showed that many people would torture a victim if they were told that it was for the good of science. Before these experiments were carried out, should these results have been assigned a low prior (because no one would suppose that they themselves would do this) or a high prior (because we know that people accept authority)? In actual practice, the method of evaluation most scientists use most of the time is a variant of a technique proposed by the statistician Ronald Fisher in the early 1900s. Roughly speaking, in this approach, a hypothesis is considered validated by data only if the data pass a test that would be failed ninety-five or ninety-nine per cent of the time if the data were generated randomly. The advantage of Fisher’s approach (which is by no means perfect) is that to some degree it sidesteps the problem of estimating priors where no sufficient advance information exists. In the vast majority of scientific papers, Fisher’s statistics (and more sophisticated statistics in that tradition) are used."|NewYoker://What Nate Silver Gets Wrong> References Category:Philosophy Category:Mathematicians Category:Science